Design of fault degree diagnosis algorithm for circuit breaker spring based on fuzzy clustering

This paper proposes a design of a fault diagnosis algorithm for circuit breaker springs based on fuzzy clustering. The features of the fault state signal are extracted by combining the methods of Intrinsic Time-Scale Decomposition and Singular Spectrum Analysis. Using the fuzzy clustering method, this study classifies circuit breaker spring faults, extracts fault features, and achieves fault degree diagnosis. The experimental results show that the algorithm has high accuracy in fault diagnosis.


Introduction
A circuit breaker is an automatic switching device used to protect power systems and electrical equipment [1].It can detect and disconnect situations where the current exceeds the rated value or malfunctions in the circuit to prevent damage to the circuit and equipment.When the current exceeds the rated value or a fault occurs, the protection unit will detect an abnormal situation and send a signal to the triggering mechanism [2].The triggering mechanism transmits the triggering signal to the main body of the circuit breaker, enabling it to quickly disconnect the circuit to protect electrical equipment and systems from overload, short circuits, and other faults [3].At the same time, the arc extinguishing system will eliminate the arc generated when the contact is disconnected.Circuit Breaker Spring is an important component commonly used for mechanical operation control in circuit breakers.It is mainly used to provide the force and rebound force for the opening and closing operation of the circuit breaker, ensuring the normal operation of the circuit breaker.Reasonable maintenance of circuit breaker springs helps to ensure normal operation and safe and reliable electrical protection of the circuit breaker.When the circuit breaker spring fails, it is difficult to control the opening and closing of the circuit breaker, leading to a threat to the safety of electrical equipment.Therefore, it is necessary to diagnose the degree of circuit breaker spring failure in order to determine the necessity of circuit breaker maintenance.
Tahvilzadeh et al. [4] put forward the simulation of a spring-driven operating mechanism, and used mechanical analysis software to obtain the stroke curve as the main signal for diagnosing mechanical faults.They established the model and verified it, solved the problem of data acquisition, and improved the accuracy and efficiency of fault detection.Shi et al. [5] put forward a hybrid method of spring energy storage state identification, which uses the Glaman angle field to represent the evolution process of dynamic characteristics.They combined the convolution block attention module and residual network to identify the state, thus realizing rapid monitoring.However, there are still some challenges and shortcomings in the current research.For example, the failure modes of circuit breaker springs are diverse and influenced by many factors, so these complexities need to be considered in the diagnosis process.In addition, the accuracy of data acquisition and processing, as well as the stability and reliability of the algorithm are also problems to be solved in current research.
Fuzzy clustering, as an unsupervised learning method, is applied in the diagnosis of circuit breaker spring fault severity [6].It can automatically learn and adapt to different fault modes and features based on the characteristics of the data.This gives it flexibility when dealing with complex circuit breaker spring faults.The fuzzy clustering algorithm can handle incomplete or noisy data, reducing the requirements for data quality.In the diagnosis of circuit breaker spring faults, due to various interferences in the data collection process, the tolerance of fuzzy clustering can make the diagnostic results more stable and reliable.

Feature extraction of 1 circuit breaker spring fault state
With the help of Internet of Things technology, multiple sensors are installed on circuit breakers [7] to monitor the fault status of circuit breaker springs and collect fault status signals.This signal has the characteristics of nonlinearity, low signal energy, and being easily submerged in noise, which is not conducive to monitoring the degree of circuit breaker spring failure.Therefore, this paper proposes a method that combines Intrinsic Time-Scale Decomposition (ITD) and Singular Spectrum Analysis (SSA) to extract the features of fault state signals and reconstruct them, thereby obtaining effective signal features of the fault degree of circuit breaker springs.The specific process is: (1) The circuit breaker spring fault status signal is set as c y , which is a time series signal with a length of M , and ITD decomposition is performed on it.The calculation formula is as follows: In the formula, q represents the nesting dimension, 2

M q d
; i J y represents the i -order inherent rotation component in ITD decomposition; Z y represents the trend component of the initial circuit breaker spring fault status signal.
By using the above formula to perform frequency domain analysis on the inherent rotation component i J y , components consistent with the characteristic frequency information are obtained.Furthermore, components of the same frequency component are collected together to obtain the signal t u y to be analyzed and processed.
(2)Using the SSA algorithm, the signal t u y to be analyzed and processed is reconstructed into a q m u dimensional phase space to obtain a trajectory matrix c F composed of m coordinate points in the phase space: The covariance matrix c Y of trajectory matrix c F is further calculated: , ,..., q A A A A corresponding to each singular value.Therefore, the original time series C composed of q th order components is: (3) Frequency domain analysis is performed on all components i R to obtain the component j R where the characteristic frequency of the circuit breaker spring fault signal is located.According to the principle of inverse reconstruction in singular spectrum analysis, the signal is superimposed and reconstructed to obtain a new matrixU .The time series after feature extraction is obtained, which is the feature of the circuit breaker spring fault signal: ,

Fault degree diagnosis algorithm based on fuzzy clustering algorithm
The fuzzy clustering algorithm used in this paper is the short-term fuzzy C-means clustering algorithm, which is further optimized on the basis of the fuzzy C-means A algorithm (FCMA) [8].The algorithm first performs segmented processing on the circuit breaker spring fault signal by frame [9].Then, it selects the characteristics of the circuit breaker spring fault signal in each segment, selects appropriate parameters, and implements spatial mapping [10].Finally, the fuzzy C-means clustering algorithm is used to implement pattern classification and recognition of the fault signal features of the circuit breaker spring, achieving the diagnosis of fault severity.
On the basis of obtaining the fault signal characteristics of the circuit breaker spring, this method uses this algorithm to classify and diagnose the fault degree of the signal features.The specific steps are as follows: (1) Feature parameter space mapping of circuit breaker spring fault signal The original time series are segmented into frames.The average and standard deviation of the characteristic parameters of the circuit breaker spring fault signal for each segment are calculated.The spatial mapping of the characteristic parameters of the circuit breaker spring fault signal is completed, and feature vectors are generated described by Q indicators: 1 2 , ,..., To avoid the phenomenon of indicator data being too small and submerged, each indicator is regularized: From this, we obtain the normalization matrix , where each row is used to describe the fuzzy set of the classification object on the indicator set.The expression is as follows: 1 2 , ,... , 1, 2,..., (2) Sample set construction and parameter initialization The distance between all circuit breaker spring fault signal samples and each cluster center is calculated, and the objective function is determined as: In the formula, , 1 The modal bundle is updated, the cluster center is recalculated, and the following equation is derived: 3) is returned to repeat clustering.On the contrary, clustering ends until the optimal clustering result is achieved, and the recognition of the fault signal characteristics of the circuit breaker spring is completed, achieving the diagnosis of the degree of the circuit breaker spring fault.The overall algorithm flow is shown in Figure 1.

Experimental results and analysis
MATLAB simulation software is used to simulate the working process and parameter changes of circuit breakers and a simulation environment is built to simulate circuit breaker spring faults.An AC power supply with an input voltage of 220 V is the power supply.A load simulator or current source is used to simulate the load and current of the circuit breaker.Current sensors, voltage sensors, temperature sensors, etc., are used to obtain relevant parameters.The experimental simulated circuit breaker spring is shown in Figure 2. Corresponding data collection and recording systems are developed using the LabVIEW programming language.The NumPy library in Python is used for data manipulation and visual analysis.Among them, the current sensor has an accuracy of 0.1 A, the voltage sensor has an accuracy of 0.1 V, the temperature sensor has an accuracy of 0.1ႏ, the simulation software has a simulation time step of 0.001 seconds, and the data collection frequency is 100 Hz.In the fuzzy clustering algorithm, the number of clusters is set to 3, the fuzzy index is set to 2, and the maximum number of iterations is 1000.A threshold is set to determine whether the algorithm is convergent, which is 0.001.
According to the above experimental environment, there are five types of faults: spring deformation or fracture, spring relaxation or loss of tension, uneven spring compression force, insufficient spring rebound force, and spring misalignment or jamming.Each type of fault occurs randomly.The operating data of the circuit breaker is collected within 24 hours of operation, which is used as the dataset.It is randomly divided into 60% as the training set to train the method in this paper, and the remaining 40% as the testing group.The testing group data is randomly divided into 5 groups for performance verification.
The accuracy of diagnosing the degree of circuit breaker spring failure under different methods is shown in Table 1: Table 1.Diagnosis accuracy of circuit breaker spring fault severity using different methods/%.

Group
The method of this paper Methods in [4] Methods in [ 1 shows that different methods can diagnose the degree of circuit breaker spring fault, but the accuracy of traditional methods is relatively low, with an average of 92.1% and 88.58%, respectively.However, the accuracy of the circuit breaker spring fault degree diagnosis proposed in this paper remains stable at a high level, with an average of 97.22%.This indicates that the method proposed in this paper has certain reliability in identifying the degree of circuit breaker spring failure.
To further verify the accuracy of the fault diagnosis method proposed in this paper, the deviation during the spring opening and closing process was used as the validation indicator to compare the error of the deviation diagnosis values under different methods, as shown in Table 2 2, it can be seen that the diagnostic range of the deviation of the method in this paper for the degree of circuit breaker spring failure is within 0.6 mm, which is much smaller than other methods.This indicates that the method proposed in this paper can effectively diagnose the degree of circuit breaker spring fault and ensure the operation detection of circuit breaker springs.
Based on the above experimental results, it can be concluded that the method proposed in this paper exhibits high accuracy and precision in diagnosing the degree of circuit breaker spring failure.This plays an important role in ensuring the operation and detection of circuit breaker springs, providing engineers and maintenance personnel with a reliable means of assessing the degree of failure.

Conclusion
This paper successfully designs a fault degree diagnosis algorithm for circuit breaker springs by using the fuzzy clustering method, combined with inherent time scale decomposition and singular spectrum analysis.This algorithm not only has high accuracy but also can effectively extract and identify the characteristics of circuit breaker spring faults, providing a more reliable guarantee for the stable operation of the power system.In the future, we will continue to optimize the algorithm, improve its diagnostic accuracy and efficiency, and explore more application scenarios in order to make greater contributions to the development of related fields.
degree of circuit breaker spring fault signal sample j C to the i th type signal sample set; > 0, J f represents the weighted index; ji j i f C q l represents the distance between signal sample j C and the center of the i th type signal sample; , K O B represents the sum of squared weighted distances between each signal sample and the clustering center, and j C represents the weight of the signal sample.The main criterion for clustering is to achieve the minimum value of the objective function , K O B .Firstly, it is necessary to construct a Lagrange function to calculate the membership function ji o .The calculation method is as follows:

Figure 1 .
Figure 1.Overall flow chart of the algorithm.

Figure 2 .
Figure 2. Actual diagram of circuit breaker spring.
Where I and B respectively represent two orthogonal left and right singular matrices; / represents the singular value of the matrix, and 3

Table 2 .
: Deviation diagnostic values for the degree of circuit breaker spring failure using different methods/mm.